You are driving down the highway late one night at 20 m/s when a deer steps onto the road 35 m in front of you. Your reaction time before stepping on the brakes is 0.50 s , and the maximum deceleration of your car is 10 m/s2 . How much distance is between you and the deer when you come to a stop?
You found the distance that you will cover while braking. You can use the expected amount of time for braking to check your answer for distance.
Using the information given in the introduction and the value for distance that you found above, determine the time required for you to stop once you press the brakes. Note that the time for braking is just the time interval t3−t2.
d1 = 35-Vo*T = 35-20*0.5 = 25 m = distance from deer when braking starts,
V^2 = Vo^2 + 2a*d2 = 0.
20^2 + (-20)d2 = 0,
d2 = 20 m. = stopping distance.
d = d1-d2 = 25-20 = 5 m. from deer.
To determine the time required for you to stop once you press the brakes, we need to consider the time interval between t3 and t2, where t3 is the time when you start braking and t2 is the time when you come to a stop.
Given:
Initial velocity (v0) = 20 m/s
Reaction time (t1) = 0.50 s
Maximum deceleration (a) = -10 m/s^2 (negative sign indicates deceleration)
Distance to the deer (d) = 35 m
First, let's calculate the distance covered during your reaction time (t1):
d1 = v0 * t1
= 20 m/s * 0.50 s
= 10 m
Next, we need to calculate the distance covered while decelerating:
The formula to calculate the distance covered while decelerating is:
d2 = (v0^2 - vf^2) / (2 * a)
Since we want to come to a stop, the final velocity (vf) is 0 m/s. Therefore, we have:
d2 = (v0^2 - 0^2) / (2 * a)
= (20^2 - 0^2) / (2 * -10)
= (400 - 0) / -20
= -20 m
Now, to find the total distance covered (d_total) before coming to a stop, we add d1 and d2:
d_total = d1 + d2
= 10 m + (-20 m)
= -10 m
However, distance cannot be negative in this context, so we take the absolute value:
d_total = |-10 m|
= 10 m
Therefore, the distance between you and the deer when you come to a stop is 10 meters.
To find the distance between you and the deer when you come to a stop, we can break down the problem into several steps.
Step 1: Calculate the distance covered during your reaction time.
Since you have a reaction time of 0.50 s before stepping on the brakes, the distance covered during this time can be calculated using the formula:
Distance = Speed * Time
Distance = 20 m/s * 0.50 s = 10 meters
Step 2: Calculate the distance covered while braking.
To calculate the distance covered while braking, we can use the formula:
Distance = Initial Velocity * Time + (1/2) * Acceleration * Time^2
In this case, the initial velocity is 20 m/s, the deceleration (acceleration) is -10 m/s^2 (negative because it's deceleration), and the time taken to stop is the time interval t3 - t2.
We know that the initial velocity is 20 m/s and the maximum deceleration is 10 m/s^2, but we need to find the time taken to stop. Since the problem mentions the maximum deceleration, we can assume that the car decelerates at a constant rate until it comes to a stop.
To find the time taken to stop, we can use the formula:
Time = Change in Velocity / Acceleration
The change in velocity is the difference between the initial velocity and the final velocity, which is 0 m/s when the car comes to a stop.
Change in Velocity = Final Velocity - Initial Velocity
Change in Velocity = 0 m/s - 20 m/s = -20 m/s
Time = Change in Velocity / Acceleration
Time = -20 m/s / -10 m/s^2 = 2 s
Now, we know that the time taken to stop is 2 s.
Step 3: Calculate the total distance between you and the deer when you come to a stop.
The total distance is the sum of the distance covered during your reaction time and the distance covered while braking.
Total Distance = Distance during reaction time + Distance during braking
Total Distance = 10 meters + Distance during braking
We know that the distance covered while braking can be calculated using the formula mentioned in step 2:
Distance = Initial Velocity * Time + (1/2) * Acceleration * Time^2
Plugging in the values:
Distance = 20 m/s * 2 s + (1/2) * (-10 m/s^2) * (2 s)^2
Distance = 40 meters - 20 meters = 20 meters
Therefore, when you come to a stop, there will be 20 meters between you and the deer.